Fixed-Time Adaptive Parameter Estimation for Hammerstein Systems Subject to Dead-Zone

Abstract

The Hammerstein model has proven its ability for modeling many industrial servo systems, but the corresponding parameter estimation remains as a challenging problem, especially for the purpose of achieving fast convergence. This paper presents a fixed-time (FxT) adaptive parameter estimation scheme for Hammerstein systems with an asymmetric dead-zone to ensure the convergence of estimated parameters in fixed-time. A continuous piecewise linear (CPL) function is adopted to model the nonlinear dead-zone dynamics to remedy the use of intermediate variable. To avoid using the system state information, a K-filter is used to construct a relationship between the unknown system parameters and the input/output signals. Then a new adaptive law based on the parameter error and the FxT scheme is developed to online estimate the lumped unknown parameters and ensure the fixed-time convergence, where an online updated auxiliary variable of regressor is suggested to eliminate the impact of the regressor on the convergence performance. Both numerical simulations and experimental results are given to demonstrate the effectiveness of proposed methods.